Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems

DOI10.4310/jdg/1214436700zbMath0497.32025OpenAlexW1583669122WikidataQ115188071 ScholiaQ115188071MaRDI QIDQ1170677

Yum-Tong Siu

Publication date: 1982

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214436700

zbMATH Keywords

vanishing theoremsHermitian bundlenegative tangent bundleLefschetz theoremscompact quotient of bounded symmetric domaincomplex-analyticity of harmonic mapsharmonic maps between Kaehler manifoldsholomorphicity of harmonic mapsstrongly hyper-q-convex boundary

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) (q)-convexity, (q)-concavity (32F10) Local differential geometry of Hermitian and Kählerian structures (53B35) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Plurisubharmonic functions and generalizations (32U05) Vanishing theorems (32L20) Questions of holomorphy and infinite-dimensional manifolds (58B12)

Related Items (65)

On the Applications of Bochner-Kodaira-Morrey-Kohn Identity ⋮ Compact Kähler manifolds with nonnegative curvature operator ⋮ The holomorphic or anti-holomorphic character of harmonic maps into irreducible compact quotients of polydiscs ⋮ Estimates for the \(\bar\partial\)-Neumann problem and nonexistence of \(C^2\) Levi-flat hypersurfaces in \(\mathbb{C} P^n\) ⋮ A non-existence theorem for pluriharmonic maps of finite energy ⋮ On the rigidity of certain discrete groups and algebraic varieties ⋮ Orbifolds, special varieties and classification theory. ⋮ Holomorphicity of minimal submanifolds in complex space forms ⋮ On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps ⋮ Pluriharmonic maps of maximal rank ⋮ 𝐿²-metrics, projective flatness and families of polarized abelian varieties ⋮ Local structure of Brill-Noether strata in the moduli space of flat stable bundles ⋮ Extension with log-canonical measures and an improvement to the plt extension of Demailly-Hacon-Păun ⋮ A global moduli space of ample subvarieties on compact Kähler manifolds with very strongly negative curvature ⋮ \((1,1)\)-geodesic maps into Grassmann manifolds ⋮ On compact splitting complex submanifolds of quotients of bounded symmetric domains ⋮ Foliations associated to harmonic maps on some complex two ball quotients ⋮ The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds ⋮ Hodge and vanishing theorems on complex Finsler vector bundles ⋮ Positive vector bundles and harmonic maps ⋮ Kodaira fibrations and beyond: methods for moduli theory ⋮ Holomorphic extensions of maps from the boundary of Kähler manifolds ⋮ Topological methods in moduli theory ⋮ On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves ⋮ On a relation between potentials for pluriharmonic maps and para-pluriharmonic maps ⋮ Positivity of Riemannian metric and the existence theorem of \(L^2\) estimates for \(d\) operator ⋮ On the Ohsawa-Takegoshi extension theorem ⋮ Division theorems for exact sequences ⋮ On the Ohsawa-Takegoshi \(L^2\) extension theorem and the Bochner-Kodaira identity with non-smooth twist factor ⋮ Toeplitz operators and Carleson measures on generalized Bargmann-Fock spaces ⋮ Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kaehler manifolds ⋮ Harmonic mappings of Kähler manifolds to locally symmetric spaces ⋮ Bogomolov-Sommese type vanishing theorem for holomorphic vector bundles equipped with positive singular Hermitian metrics ⋮ On the Ohsawa-Takegoshi \(L^2\) extension theorem and the twisted Bochner-Kodaira identity ⋮ Partial energies monotonicity and holomorphicity of Hermitian pluriharmonic maps ⋮ Comparison of the Bergman and Szegö kernels ⋮ (k, s)-POSITIVITY AND VANISHING THEOREMS FOR COMPACT KÄHLER MANIFOLDS ⋮ Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups ⋮ Integral formulas and the Ohsawa-Takegoshi extension theorem ⋮ \(L^p\)-estimates and existence theorems for the \(\bar \partial\)-operator on complete Kähler manifolds ⋮ Vanishing theorems on compact hyper-Kähler manifolds ⋮ Bochner-Kodaira techniques on Kähler Finsler manifolds ⋮ Energy estimates and Liouville theorems for harmonic maps ⋮ Optimal constant problem in the \(L^2\) extension theorem ⋮ Cohomology dimension growth for Nakano \(q\)-semipositive line bundles ⋮ Generically strongly \(q\)-convex complex manifolds ⋮ Closed range for \(\overline{\partial}\) and \(\overline{\partial}_b\) on bounded hypersurfaces in Stein manifolds ⋮ Rigidity theorem for harmonic maps with complex normal boundary conditions ⋮ Rigidity of harmonic maps of maximum rank ⋮ Laplacian on complex Finsler manifolds ⋮ Some applications of the Ohsawa-Takegoshi extension theorem ⋮ L² CASTELNUOVO–DE FRANCHIS, THE CUP PRODUCT LEMMA, AND FILTERED ENDS OF KÄHLER MANIFOLDS ⋮ RC-positivity and rigidity of harmonic maps into Riemannian manifolds ⋮ A boundary value problem for Hermitian harmonic maps and applications ⋮ The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman ⋮ Pointwise estimates for the weighted Bergman projection kernel in \({\mathbb C}^n\), using a weighted \(L^2\) estimate for the \(\bar\partial\) equation ⋮ Harmonic maps between compact Hermitian manifolds ⋮ Unnamed Item ⋮ On a curvature condition that implies a cohomology injectivity theorem of Kollár-Skoda type ⋮ A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry ⋮ Unnamed Item ⋮ Geometric superrigidity ⋮ Bounds on the dimension of \(L^ 2\) holomorphic sections of vector bundles over complete Kähler manifolds of finite volume ⋮ Continuation of positive, closed currents and analytic sets ⋮ On the existence of bounded holomorphic functions on complete Kähler manifolds

This page was built for publication: Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems